Analytical Volume Analysis for the Finite-time Controllable Region of the Linear Discrete-time Systems
Abstract
In this paper, the works on the analytical volume analysis for the controllable regions of the linear discrete-time (LDT) systems in papers zhaomw202001 and zhaomw202004 are discussed further and a new theorem on the analytical computing for the finite-time controllability zonotope (controllable region) of LDT systems are proven. And then, three analytical factors describing the control capability of the systems are deconstructed successfully from the analytical volume expression of the controllable region. Finally, the theorem is generalized to three cases: the narrow controllable region, the matrix A with n negative eigenvalues, the linear continuous-time systems.
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